Scholars recognize that time-series-cross-section data typically correlate across time and space, yet they tend to model temporal dependence directly while addressing spatial interdependence solely as nuisance to be “corrected” (FGLS) or to which to be “robust” (PCSE). We demonstrate that directly modeling spatial interdependence is methodologically superior, offering efficiency gains and generally helping avoid biased estimates even of “non-spatial” effects. We first specify empirical models representing two modern approaches to comparative and international political economy: (context-conditional) open-economy comparative political-economy (i.e., common stimuli, varying responses) and international political-economy, which implies interdependence (plus closed-economy and orthogonal-open-economy predecessors). Then we evaluate four estimators—non-spatial OLS, spatial OLS, spatial 2SLS-IV, and spatial ML—for analyzing such models in spatially interdependent data. Non-spatial OLS suffers from potentially severe omitted-variable bias, tending to inflate estimates of common-stimuli effects especially. Spatial OLS, which specifies interdependence directly via spatial lags, dramatically improves estimates but suffers a simultaneity bias, which can be appreciable under strong interdependence. Spatial 2SLS-IV, which instruments for spatial lags of dependent variables with spatial lags of independent variables, yields unbiased and reasonably efficient estimates of both common-stimuli and diffusion effects, when its conditions hold: large samples and fully exogenous instruments. A tradeoff thus arises in practice between biased-but-efficient spatial OLS and consistent- (or, at least, less-biased-) but-inefficient spatial 2SLS-IV. Spatial ML produces good estimates of non-spatial effects under all conditions but is computationally demanding and tends to underestimate the strength of interdependence, appreciably so in small-N samples and when the true diffusion-strength is modest. We also explore the standard-error estimates from these four procedures, finding sizable inaccuracies by each estimator under differing conditions, and PCSE’s do not necessarily reduce these inaccuracies. By an accuracy-of-reported-standard-errors criterion, 2SLS-IV seems to dominate. Finally, we explore the spatial 2SLS-IV estimator under varying patterns of interdependence and endogeneity, finding that its estimates of diffusion strength suffer only when a condition we call cross-spatial endogeneity, wherein dependent variables (y’s) in some units cause explanatory variables (x’s) in others, prevails.

In estimating incumbency advantage and campaign spending effect, simultaneity problem is composed of stochastic dependence and parametric dependence. Scholars have tried to solve the former, while the present paper intends to tackle the latter. Its core idea is to estimate parameters by maximizing likelihood of all endogenous variables (vote, both parties' candidate qualities and campaign spending) simultaneously. In order to do it, I take advantage of theories of electoral politics rigorously, model each endogenous variables by the others (or their expectation), derive Bayesian Nash equilibria, and plug them into my estimator. I show superiority of my model compared to the conventional estimators by Monte Carlo simulation. Empirical application of this model to the recent U.S. House election data demonstrates that incumbency advantage is smaller than previously shown and that entry of incumbent and strong challenger is motivated by electoral prospect.